## Related Topics

- How to Translate Phrases into an Algebraic Statement
- How to Simplify Polynomial Expressions
- How to Use the Distributive Property
- How to Evaluate One Variable
- How to Evaluate Two Variables

## Step by step guide to simplifying variable expressions

- In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x, y, z, a, b, c, m\) and \(n\).
- An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
- In an expression, we can combine “
**like**” terms. (values with same variable and same power)

### Simplifying Variable Expressions – Example 1:

Simplify this expression. \(2x + \ 3x + \ 4=\)\(?\)

**Solution:**

Combine “**like**” terms. Then: \(2 x \ + \ 3 x \ = 5x \) (remember you cannot combine variables and numbers).

Then: \(2x + 3 x + \ 4=5x + \ 4\) (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 2:

Simplify this expression. \(12 \ – \ 3x^{2} \ + 5 x + \ 4 x^{2}=\)\(?\)

**Solution:**

Combine “**like**” terms: \(- \ 3x^{2} \ + 4 x^{2}=x^{2}\)

Then: \(12 \ – \ 3 x^{2} \ + \ 5x + 4 x^{2}\) \(=12 \ + x^2 + 5x\). Write in standard form (biggest powers first): \(x^2 \ + 5 x + \ 12\)

### Simplifying Variable Expressions – Example 3:

Simplify this expression. \((10x+2x+3)=\)\(?\)

**Solution:**

Combine “**like**” terms: \((10x+2x)=12x\)

Then: \((10x+2x+3)=12x+3\) (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 4:

Simplify this expression. \(12-3x^2+9x+5x^2=\)\(?\)

**Solution:**

Combine “**like**” terms: \(-3x^2+5x^2=2x^2\)

Then: \(12-3x^2+9x+5x^2=12+2x^2+9x\). Write in standard form (biggest powers first): \(2x^2+9x+12\)

## Exercises for Simplifying Variable Expressions

### Simplify each expression.

- \(\color{blue}{– 2 – x^2 – 6x^2}\)
- \(\color{blue}{ 3 + 10x^2 + 2}\)
- \(\color{blue}{ 8x^2 + 6x + 7x^2}\)
- \(\color{blue}{5x^2 – 12x^2 + 8x }\)
- \(\color{blue}{– 2(4 – 6x) – 3x }\)
- \(\color{blue}{ 9 – 2x + 5x + 2}\)

### Download Simplifying Variable Expressions Worksheet

## Answers

- \(\color{blue}{– 7x^2 – 2}\)
- \(\color{blue}{10x^2 + 5}\)
- \(\color{blue}{15x^2 + 6x}\)
- \(\color{blue}{– 7x^2 + 8x}\)
- \(\color{blue}{9x \ – 8 }\)
- \(\color{blue}{3x \ + 11}\)

### More math articles

- Overview of the ACT Mathematics Test
- Top 10 Tips to Overcome HiSET Math Anxiety
- How long Is the ACT Test?
- 8th Grade STAAR Math Worksheets: FREE & Printable
- What Level of Math is Tested on the PSAT/NMSQT?
- Best Books for Students Preparing for the SAT Math Test
- 8th Grade STAAR Math FREE Sample Practice Questions
- Algebra Puzzle – Challenge 32
- What Skills Do I Need for The CBEST Math Test?
- Top 5 Free Websites for Pre-Algebra Math Preparation

Elena–I don’t think this site is effortless. It’s effortful!

Effortless Math Team–Thank you for your feedback Elena! We are constantly working on our website to improve its quality. If you have any suggestions please let us know.

Denise–I have already shared this site with parents of my tutoring students. Parents are always looking for good suggestions and your other materials for purchase look very nice, too. I’m looking forward to helping my students as we work through this prealgebra material, together. I’ll make sure I share the actual links with my students and not pictures of the worksheets!

Effortless Math Team–Thank you Denise for using our math resources!